A Global Positioning System ("GPS") uses transmission of coded radio signals from a plurality of Earth-orbiting satellites. A single passive receiver of such signals is capable of determining receiver absolute position in an Earth-centered, Earth-fixed coordinate reference system utilized by the GPS. A configuration of two or more receivers can be used to accurately determine the relative positions between the receivers or stations. This method, known as differential positioning, is far more accurate than absolute positioning, provided that the distances between these stations are substantially less than the distances from these stations to the satellites, which is the usual case.
In differential positioning, many of the errors in the GPS that compromise the accuracy of absolute position determination are similar in magnitude at stations that are physically close. The effect of these errors on the accuracy of differential position determination is therefore substantially reduced by a process of partial error cancellation.
The GPS satellites transmit spread-spectrum signals on the L1 frequency (f.sub.L1 =1575.42 MHz) and on the L2 frequency (f.sub.L2 =1227.6 MHz). The L1 signal is modulated by two pseudo-random noise (PRN) codes, known as the C/A-code (chip rate of 1.023 MHz) and the P-code (chip rate of 10.23 MHz). The L2 signal is modulated only by the P-code. Most GPS receivers generate replica PRN codes to facilitate coherent demodulation of the received GPS signals. Accepted methods for generating the C/A-code and P-code are available to designers of GPS receivers in the document GPS Interface Control Document ICD-GPS-200, Rockwell International Corporation, Satellite Systems Division, Revision A, 26 Sep. 1984, which is incorporated by reference herein. The operators of the GPS satellites can substitute for the P-code an encrypted version of the P-code, called the Y-code. The Y-code would be transmitted on both the L1 and L2 frequencies.
In addition to transmitting the PRN codes, the GPS satellites also transmit navigational data at 50 Baud. These data are ephemerides and almanac of the satellites and are used to calculate accurate satellite positions in an Earth-centered, Earth-fixed coordinate system. These positions are utilized by absolute and differential positioning methods.
Numerous applications require determination of the relative position between stations. Geodetic survey applications can be subdivided into: (1) applications in which all of the stations receiving the GPS signals are stationary, referred to as static surveying; and (2) applications in which one or more of the stations is moving relative to other stations, referred to as kinematic surveying. The latter class of applications is increasingly popular, because many more relative station positions can be determined in a fixed time of observation of the GPS satellites. Differential positioning applications, such as aerial and marine surveying, are kinematic surveying by definition.
If the stations have a method of inter-station communication, the relative positions between stations can be computed in real-time. Data need not be stored and post-processed after a surveying mission in applications that require real-time relative position, such as precision approach landing of aircraft and piloting of marine vessels.
One or more stations is designated as a reference station, and can be fixed at a known position or can be moving. The positions of the other stations, known as the roving stations, which also may be stationary or moving, are calculated relative to the reference station(s). The approximate absolute positions of the reference stations are required. These positions, if unknown, can be computed using established absolute position determination methods that utilize measurement of PRN code phases.
The highest accuracy obtainable in differential positioning requires measurement and utilization of the received carrier phase of the L1 and L2 signals at precisely known times, derived from clocks within the GPS receivers. Many techniques for processing GPS data for kinematic surveying applications use only these carrier phase measurements in the calculation of differential positions, with measurement of PRN code phases only used to calculate accurate time-marks for the carrier phase measurements.
A major difficulty occurs if only the carrier phase measurements are utilized in the calculation of differential positions. These measurements are ambiguous. The measurement from each satellite includes measurement of a fractional phase .phi.(0.degree.&lt;.phi.&lt;360.degree.) plus an additional integer number N of whole cycles of phase. This integer number or integer ambiguity, hereafter referred to as a phase integer, cannot be directly measured by a receiver.
For kinematic surveying, a process known as integer initialization can be used to establish the initially unknown phase integers. One approach is to set the receivers at marks whose relative positions are already known. These relative positions are also known as baselines, and are defined by (x,y,z) vector components. Another approach is to allow the receivers to remain static at arbitrary marks for a period of time, to allow static surveying techniques to be used to resolve the phase integers. Another approach is to exchange the antennas between receivers set at arbitrary marks without disturbing the signal reception during the exchange of antennas. Once the phase integers are resolved, differential positioning is possible with the full accuracy obtained by the carrier phase measurements. However, if signal lock cannot be maintained on four satellites with suitable geometry, the initialization procedure must be repeated.
All of the initialization procedures mentioned above require the receivers to remain stationary relative to each other, and some of these procedures are time-consuming. Thus, these methods cannot be used on the moving platforms encountered in aerial and marine kinematic surveying.
In U.S. Pat. No. 4,463,357, MacDoran discloses maximization of the cross-correlation of two identical signals, modulated at different carrier frequencies, arriving at a receiver, to determine the time difference of arrival of the signals. This time difference arises from a difference in phase delay for passage of the two modulated signals through the ionosphere. This technique is used to measure the columnar electron content of the ionosphere.
Fowler, in U.S. Pat. No. 4,754,283, discloses use of a codeless sounding device to monitor wind velocity and wind direction, using a transmitter whose position is known in space, a first receiver whose position on the ground is known and fixed, and a second receiver that is airborne and carried by the locally prevailing wind. Wind direction and magnitude are determined by comparison of Doppler-shifted signals received at the two receivers.
In U.S. Pat. No. 4,797,677, MacDoran et al disclose a method for determining pseudorange of a receiver positioned on the ground from Doppler shift measurements of signals transmitted by two or more satellites and received by a ground-based receiver, whose position is at least partly unknown. A coarse range measurement is first made, and this coarse range is required to be accurate to within one third of a wavelength. A Doppler-derived pseudorange is divided by signal wavelength to produce a phase, measured in wavelength cycles, that includes an integer part and a fractional part that contributes to fractional phase.
Dynamic differential position determination, using carrier phase measurements at both the carrier frequencies f.sub.L1 and f.sub.L2, is disclosed by Hatch in U.S. Pat. No. 4,812,991. Hatch determines uncorrected pseudoranges from each of four or more satellites to a reference receiver of known position and to a roving receiver, both on the ground. Hatch also uses L1 and L2 carrier phase differences and filters the L1 and L2 pseudorange information and further processes the filtered pseudorange data to obtain smoothed range data from each satellite to each receiver. Both L1 and L2 pseudoranges are required. Differences of the smoothed range data and theoretical range data are formed for each satellite-reference receiver combination to aid in determining the position of the roving receiver.
Counselman discloses use of Doppler-shift measurements of signals emitted from two or more satellites and received by two or more ground-based receivers in U.S. Pat. No. 4,870,422. Two carrier frequency signals are transmitted by each satellite, and the received signals are divided into upper and lower sideband signals for further processing to determine a vector separating the two ground-based satellites.
Counselman, in U.S. Pat. No. 4,912,475, discloses use of double difference phase biases for determination of orbital information for each of a plurality of satellites, using three or more ground-based receivers whose positions are known and fixed. The ratios of the receiver baseline distances must satisfy special constraints in this method.
A method is required that will permit accurate differential positioning on stationary or moving platforms by resolving the unknown phase integers associated with carrier phase measurements. In addition, the method should not require a time-consuming or complicated special initialization procedure.